• Kyungpook Mathematical Journal
• /
• v.62 no.3
• /
• pp.425-436
• /
• 2022

In this paper we introduce the notion of 2-absorbing primary ideals of a commutative semigroup. We establish the relations between 2-absorbing primary ideals and prime, maximal, semiprimary and 2-absorbing ideals. We obtain various characterization theorems for commutative semigroups in which 2-absorbing primary ideals are prime, maximal, semiprimary and 2-absorbing ideals. We also study some other important properties of 2-absorbing primary ideals of a commutative semigroup.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.1
• /
• pp.27-37
• /
• 2000

In this paper, we will introduce the pan-dual generalized fuzzy integral of a commutative isotonic semigroup-valued functions, which is generalized of the (DG) fuzzy integral and investigate the fundamental properties of this kind of fuzzy integral.

• Journal of the Chungcheong Mathematical Society
• /
• v.11 no.1
• /
• pp.173-183
• /
• 1998

In this paper, we introduce the pan-generalized fuzzy integral of a commutative isotonic semigroup-valued function, which is generalization of the (G) fuzzy integral and investigate the fundamental properties of this kind of fuzzy integral.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.829-839
• /
• 2019

Let S be a commutative semigroup with 0 and 1. A proper ideal P of S is weakly prime if for $a,\;b{\in}S$, $0{\neq}ab{\in}P$ implies $a{\in}P$ or $b{\in}P$. We investigate weakly prime ideals and related ideals of S. We also relate weakly prime principal ideals to unique factorization in commutative semigroups.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.1
• /
• pp.239-246
• /
• 2015

If for every elements x and y of an associative algebraic structure (S, ${\cdot}$) there exists a positive integer r such that $ab=b^ra$, then S is called quasi-commutative. Evidently, every abelian group or commutative semigroup is quasi-commutative. Also every finite Hamiltonian group that may be considered as a semigroup, is quasi-commutative however, there are quasi-commutative semigroups which are non-group and non commutative. In this paper, we provide three finitely presented non-commutative semigroups which are quasi-commutative. These are the first given concrete examples of finite semigroups of this type.

• Kyungpook Mathematical Journal
• /
• v.46 no.2
• /
• pp.231-233
• /
• 2006

We characterize those commutative semigroups S such that every non-isomorphic homomorphic image of S has smaller cardinality than S. We also characterize commutative groups with the same property.

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• pp.667-679
• /
• 2007

We study the prime ideal structure of the direct sum of directed system of rings indexed by a commutative semigroup which is nilpotent extension of a group.

• Journal of applied mathematics & informatics
• /
• v.41 no.4
• /
• pp.707-722
• /
• 2023

The purpose of this paper is to obtain the commutativity of a gamma dominion for a commutative gamma semigroup by using Isbell zigzag theorem for gamma semigroup and we prove some gamma semigroup identities are preserved under epimorphism. Moreover, we extend epimorphism, dominion and Isbell zigzag theorem for partially ordered semigroup to partially ordered gamma semigroup.

• Korean Journal of Mathematics
• /
• v.7 no.1
• /
• pp.111-116
• /
• 1999

In this paper, we introduce the concepts of quasi retract ideals and quasi retract topological semigroups which are weaker than those of retract ideals and retract topological semigroups, respectively. We prove that every $n$-th power ideal of a commutative power cancellative power ideal topological semigroup is a quasiretract ideal.

• Kyungpook Mathematical Journal
• /
• v.51 no.1
• /
• pp.37-42
• /
• 2011

Let M be an R-module and S a semigroup. Our goal is to discuss zero-divisors of the semigroup module M[S]. Particularly we show that if M is an R-module and S a commutative, cancellative and torsion-free monoid, then the R[S]-module M[S] has few zero-divisors of size n if and only if the R-module M has few zero-divisors of size n and Property (A).